Geodesic
Asymptotic behavior of a selfinteracting random walk
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 126-132 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a simple one-dimensional random walk with the statistical weight of each sample path given by $\pi_t(\omega)=\exp\{-\beta\sum_{0\leq i, where $\beta$ has the meaning of negative temperature, and $V$ is a nonnegative decreasing function with finite support. We show that for $\beta>\beta_0$ the distribution of $\omega_n$ is concentrated in the area $\{|\omega_n|>c\,n\}$, where $c=c(\beta)>0$, and for $\beta<0$ every sample path becomes localized, in the sense that $\omega_n$ never leaves some fixed interval.
Keywords: potential, random walk, self-repulsive random walk, asymptotic behavior. 
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S. A. Nadtochii. Asymptotic behavior of a selfinteracting random walk. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 126-132. http://geodesic.mathdoc.fr/item/TVP_2006_51_1_a8/

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